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Four statements are given (A is mass number): I. The volume of a nucleus is proportional to $A^{1/3}$. II. The volume of a nucleus is proportional to A. III. The difference in mass of an atom and its nucleus is called the mass defect. IV. The difference in mass of a nucleus and its constituents is called the mass defect. Choose the CORRECT answer from the options given below:
A
II and IV are true, but I and III are false
B
I and IV are true, but II and III are false
C
I and III are true, but II and IV are false
D
II and III are true, but I and IV are false
Detailed Solution
I. False, because $V \propto A$ (since $R \propto A^{1/3}$)
II. True, because $V \propto R^3 \propto A$
III. False, because (mass of atom $-$ mass of nucleus) $\approx$ total mass of electrons, not the mass defect
IV. True, because $\Delta m$ = (total mass of constituents $-$ mass of nucleus)
So II and IV are true, but I and III are false.